D.5.5 goettsche_lib

Library:

goettsche.lib

Purpose:

Drezet's formula for the Betti numbers of the moduli space of Kronecker modules; Goettsche's formula for the Betti numbers of the Hilbert scheme of points on a surface; Nakajima's and Yoshioka's formula for the Betti numbers of the punctual Quot-schemes on a plane or, equivalently, of the moduli spaces of the framed torsion-free planar sheaves; Macdonald's formula for the symmetric product

Author:

Oleksandr Iena, o.g.yena@gmail.com

References:

[1] Drezet, Jean-Marc Cohomologie des varie'te's de modules de hauter nulle. Mathematische Annalen: 281, 43-85, (1988).

[2] Goettsche, Lothar, The Betti numbers of the Hilbert scheme of points on a smooth projective surface.
Mathematische Annalen: 286, 193-208, (1990).

[3] Macdonald, I. G., The Poincare polynomial of a symmetric product, Mathematical proceedings of the Cambridge Philosophical Society: 58, 563-568, (1962).

[4] Nakajima, Hiraku; Lectures on instanton counting, CRM Proceedings and Lecture Notes, Yoshioka, Kota Volume 88, 31-101, (2004).

Procedures:

D.5.5.1 GoettscheF		The Goettsche's formula up to n-th degree
D.5.5.2 PPolyH		Poincare Polynomial of the Hilbert scheme of n points on a surface
D.5.5.3 BettiNumsH		Betti numbers of the Hilbert scheme of n points on a surface
D.5.5.4 NakYoshF		The Nakajima-Yoshioka formula up to n-th degree
D.5.5.5 PPolyQp		Poincare Polynomial of the punctual Quot-scheme of rank r on n planar points
D.5.5.6 BettiNumsQp		Betti numbers of the punctual Quot-scheme of rank r on n planar points
D.5.5.7 MacdonaldF		The Macdonald's formula up to n-th degree
D.5.5.8 PPolyS		Poincare Polynomial of the n-th symmetric power of a variety
D.5.5.9 BettiNumsS		Betti numbers of the n-th symmetric power of a variety
D.5.5.10 PPolyN		Poincare Polynomial of the moduli space of Kronecker modules N (q; m, n)
D.5.5.11 BettiNumsN		Betti numbers of the moduli space of Kronecker modules N (q; m, n)